So I am approaching level 30 and have quite a few questions:
Daedra: Is this a whole sideline of quests? Does completing them give one daedra hearts that can be used to make weapons/armor?
Most of the Daedric quests are optional, but you will likely stumble onto a few simply as you travel around and dungeon dive. Daedra hearts can be found randomly in places but you will need them to forge Daedric armor, if you want to make some.
Armor: I'm rocking light but only up to about 130 at best. Is this something I need to concentrate on improving? Is it better to go ahead and commit to smithing, or better to find/buy?
You pretty much have to commit to an armor path if you want to eventually have the best stuff...with light going through the glass into dragonscale while heavy goes from ebony to Daedric to Dragonplate. You really won't have enough perks to upgrade both sides without really hurting your other ability tree progression. To that end, if you're heading along the light side, Daedra hearts won't matter much for you. I would definitely commit to smithing, because it's really easy to create and upgrade armor and weapons.
Weapons: Currently using a blades sword, but thinking it would be nice to get something really badass that is a two-handed blade. Any sidequests that give really good weapons?
Another consideration is how you level fighting. You can certainly use both two and one-handed weapons, but again it'll make it harder for you to maximize your perks trees. It's very easy to get better weaponry, as it will be dropped on quests, in trunks, and of course you can buy stuff from merchants and steal stuff. Most types of goods level with you, so you'll start seeing better stuff everywhere as you level up. I routinely find ebony and glass armor and weapons now, and when you get to Level 50 even Dragon Plate and Dragonscale start appearing at times.
Loot: Frankly I am really disappointed in the quality of the loot I'm finding. Are people finding all kinds of good stuff that I am missing, or just enchanting and smithing their own?
Are you pickpocketing, lockpicking and stealing? I found that to be the easiest way to get really good stuff quickly, but not the only way. As I said in the prior comment, the loot you find levels with you.
Spells: My two best destruction are Ice Storm and Fireball. Should I be focusing on leveling up the perks in destruction or getting more powerful spells?
This is entirely up to you, but as with all things, if you opt to be a jack of all trades, you're going to be a master of none. I eschewed magic almost entirely so I could focus on my thief, alchemy/smithing and one-handed/archery trees. There wasn't enough room to add a magic tree or two, as well. Now that said, I do still level them, particularly when I come across a trainer. It's cheap to train with people until you're Level 50, so I routinely train five times (the max per level) with any trainer I'm not high on, and pickpocket my gold back between training sessions so it ends up being free.
Shouts: Opinions on going out and gaining as many as possible via fast travel or acquiring them naturally by completing quests?
As with most things Skyrim, this is entirely up to you. There are certain shouts you will learn as part of the main quest, but all the rest are optional. I've stumbled onto a bunch, sought out a few others, and to be honest, I primarily use Unrelenting Force most of the time. But I may find more use for them as I get toward the later stages of the Main Quest. Shouts, Dragon Priest Masks, Guild Paths, are all optional really -- but add lots of hours of entertainment if you want them to.